Multiband antennas which allow reception and transmission of radiation in at least two different frequency ranges are known from the prior art. By way of example, the document DE 198 23 749 A1 discloses a dual-polarized multiband antenna which has first and second antenna elements. The first and second antenna elements transmit and receive in different frequency ranges and comprise dual-polarized dipole antenna elements which are arranged on a reflector and transmit and receive in polarizations which are aligned at +45° and −45° to the vertical. In the case of the multiband antenna which is disclosed in this document, the first antenna elements are in the form of cruciform dipoles which transmit and receive in an upper frequency band. The antenna elements in the lower frequency band are dipole squares, with one cruciform dipole being arranged in each dipole square. The radiation characteristics of the first and second antenna elements can be varied by appropriate shaping of the reflector, although it is not possible to simultaneously optimize the radiation characteristics for the upper and lower frequency bands.